Feb 2007
3.1
Aero 2
Signals & Systems (Part 2)
Lecture 3: Boolean Algebra
Professor Peter Cheung
Department of EEE, Imperial College London
(Floyd 4.1-4.4, 5.2-5.4)
(Tocci 3.8-3.14)
Feb 2007
Aero 2
Signals & Systems (Part 2)
Points Addressed in this Lecture
•
Theorems & rules in Boolean algebra
• DeMorgan’s Theorems
•
Universality of NAND & NOR gates
•
Active low & Active high
•
Digital Integrated Circuits
Feb 2007
3.3
Aero 2
Signals & Systems (Part 2)
Laws of Boolean Algebra
•
Commutative Laws
•
Associative Laws
•
Distributive Law
Feb 2007
3.4
Aero 2
Signals & Systems (Part 2)
Commutative Laws of Boolean Algebra
A + B = B + A
A
•
B = B
•
A

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Feb 2007
3.5
Aero 2
Signals & Systems (Part 2)
Associative Laws of Boolean Algebra
A + (B + C) = (A + B) + C
A
•
(B
•
C) = (A
•
B)
•
C
Feb 2007
3.6
Aero 2
Signals & Systems (Part 2)
Distributive Laws of Boolean Algebra
A
•
(B + C) = A
•
B + A
•
C
A (B + C) = A B + A C
Feb 2007
3.7
Aero 2
Signals & Systems (Part 2)
Rules of Boolean Algebra
Feb 2007
3.8
Aero 2
Signals & Systems (Part 2)
Rules of Boolean Algebra
OR Truth Table
AND Truth Table
•
Rule 1
•
Rule 2
•
Rule 3
•
Rule 4